Deconfinement Phase Transition in Hot and Dense QCD at Large N

TL;DR

This paper proposes that the confinement-deconfinement phase transition in large N QCD is driven by a sudden change in the theta dependence, supported by holographic models, quantum field theory, and lattice results, and analyzes critical parameters.

Contribution

It introduces a conjecture linking the phase transition to theta dependence changes, supported by multiple theoretical and numerical approaches, and studies the transition in the large N limit.

Findings

Phase transition coincides with a sharp change in theta dependence.

Critical temperature and chemical potential are estimated from controlled instanton calculations.

Holographic models and lattice results support the conjecture.

Abstract

We conjecture that the confinement- deconfinement phase transition in QCD at large number of colors $N$ and $N_f\ll N$ at $T\neq 0$ and $\mu\neq 0$ is triggered by the drastic change in $\theta$ behavior. The conjecture is motivated by the holographic model of QCD where confinement -deconfinement phase transition indeed happens precisely at $T=T_c$ where $\theta$ dependence experiences a sudden change in behavior. The conjecture is also supported by quantum field theory arguments when the instanton calculations (which trigger the $\theta$ dependence) are under complete theoretical control for $T>T_c$, suddenly break down immediately below $T<T_c$ with sharp changes in the $\theta$ dependence. Finally, the conjecture is supported by a number of numerical lattice results. We employ this conjecture to study confinement -deconfinement phase transition of hot and dense QCD in large $N$ limit by analyzing the $\theta$ dependence. We estimate the critical values for $T_c$ and $\mu_c$ where the phase transition happens by approaching the critical values from the hot and/or dense regions where the instanton calculations are under complete theoretical control. We also describe some defects of various codimensions within a holographic model of QCD by focusing on their role around the phase transition point.